Abstract
By taking into account the nonlinear effect
of the cause, the inner noise effect, and the
measurement distortion effect in the observed
variables, the post-nonlinear (PNL) causal
model has demonstrated its excellent performance
in distinguishing the cause from effect.
However, its identifiability has not been
properly addressed, and how to apply it in
the case of more than two variables is also a
problem. In this paper, we conduct a systematic
investigation on its identifiability in the
two-variable case. We show that this model is
identifiable in most cases; by enumerating all
possible situations in which the model is not
identifiable, we provide sufficient conditions
for its identifiability. Simulations are given
to support the theoretical results. Moreover,
in the case of more than two variables, we
show that the whole causal structure can be
found by applying the PNL causal model to
each structure in the Markov equivalent class
and testing if the disturbance is independent
of the direct causes for each variable. In this
way the exhaustive search over all possible
causal structures is avoided.
